Modeling the inter-individual variability of single-stemmed plant development

Modeling the development of single-stemmed plants is classically done by expressing the number of phytomers in the main axis as a function of the thermal time. In many cases, a strong inter-individual variability is encountered, that cannot be straightforwardly associated to any environmental or micro-environmental factors. We propose a methodological framework to describe the heterogeneity of individual responses in a population by hierarchical or mixed-effect models : Some regression parameters are random variables identically distributed in the population. The method is illustrated using experimental data collected on young Acacia erioloba plants, grown in CEREEP greenhouse, for which two piecewise-linear models of organogenesis are identified using Expectation-Maximization (EM) algorithm and compared according to their adequacy to the data. The E-step and the M-step of the algorithm are analytic as long as the dependence is linear with respect to the individual parameters, i.e. the latent variables of the mixed-effect model. In the general case, the posterior distribution of the individual parameters cannot be analytically determined. Monte-Carlo Markov Chains are generated with Metropolis-Hasting during the E-step to estimate the distribution. Alternatively, a Laplace approximation of the posterior distribution appeared to be quite relevant in our case. Such framework will be adapted to the identification of a complete FSPM of Acacia growth combining organogenesis and functioning.